Critical speeds and buckling loads of a pre-twisted rotor

The equations of motion of a pre-twisted rotor subjected to a compressive axial load have been derived by including the effects of transverse shear, rotatory inertia and gyroscopic moments to model material removal systems which have external flutes. The finite element method is used to obtain a system of ordinary differential equations. C⁰-compatible finite elements are used to obtain the critical speeds and buckling loads for different helix angles, flute lengths and drill diameters for various support conditions. The critical speeds decrease with increasing compressive axial load. The lowest mode is associated with a critical thrust force which corresponds to a zero critical speed. This critical thrust force is the buckling load of the lowest mode of the nonrotating pre-twisted rotor.